PDE Seminar (2016/10/28):On Hamilton-Jacobi equation with initial data of the Takagi function, Yasuhiro Fujita (University of Toyama)

Date
2016-10-28 16:30 - 2016-10-28 18:00
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Yasuhiro Fujita (University of Toyama)
 
The Takagi function is an example of everywhere continuous and nowhere differentiable functions on the real line. The set of maximum points in the unit interval for the Takagi function is known to be a perfect but null set like the Cantor set.

In this talk, we consider the Cauchy problem of a Hamilton-Jacobi equation when the initial data is the Takagi function. Our aim is to investigate the set of maximum points in the unit interval for its unique viscosity solution. This solution has a beautiful structure. This talk is based on a joint work with Norikazu Yamaguchi (Toyama).